PDF BT11803 MATHEMATICAL ECONOMICS - Universiti Malaysia Sabah

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Group Members:

 BEH CHI YI (BB20110376)

 CHUA SHIN SHYUAN (BB20110099)

 LOW LAY WEN (BB20110121)

 JENTIA ANAK AMPAS (BB20110134)

 MELCDIANIE JAUSIN (BB20110652)

 ANGELINE UMANG ANAK JOHN BENJAMIN (BB20110106)

 LO SIAW HONG (BB20110201)

 NURUL FARAH AIN BINTI JUANS (BB20110595)

 EMMANUEL ESTRADA ANAK FRANCIS (BB20110628)

 SAIFUL BAHRIN BIN MANJA (BB20110162)

BT11803 MATHEMATICAL ECONOMICS

MOVIE REVIEW: THE MAN WHO KNEW INFINITY

LECTURER: DR KHAIRUL HANIM PAZIM

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"The Man Who Knew Infinity" revolves

around Ramanujan's legendary experience.

This is a biographical story about the life of a genius mathematician.

The mathematician’s name is Ramanujan and he is an Indian.

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 Ramanujan is a little Indian brother without formal education due to poor family background, but he has an unusual understanding of numbers. He wrote a lot of mathematical formulas outside of work, but no one could understand it. He found many local scholars, but no scholars were willing to write letters of recommendation for him.

 Fortunately, he met the first noble man in his life, an old Indian man who worked in a British company. This old man could understand some of his formulas. With the joint efforts of the two, the British boss finally recognized Ramanujan's calculation ability, so he wrote a letter of recommendation to the mathematician Godfrey Harold Hardy, who was a student of Trinity in Cambridge. Hardy was attracted by the formula in the letter and recommended Ramanujan to study in Cambridge.

 At that time, the arrogant white people believed that Ramanujan is a liar because there are no proofs for his research. However, Ramanujan is lucky as Hardy was impressed by Ramanujan’s abilities. Hardy always help Ramanujan in writing proofs and managed to help Ramanujan published in the London Mathematical Society.

 While Ramanujan was writing proofs, he fainted. The result from doctor was it is the early sign of Tuberculosis.

His illness was getting worse. In the end, Ramanujan successfully published his formula with the help of Hardy and accepted as a Fellow of the Royalty Society and a Fellow of Trinity College. Ramanujan’s illness returned during his journey back to India. After a year with his wife, Janaki, he died at the age of 32.

SUMMARY

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Srinivasa Ramanujan (1887 – 1920)

◦ One of the youngest elected Fellow of the Royal Society (2 May 1918)

◦ The first Indian elected as a Fellow of Trinity College, Cambridge (13 October 1918)

Significant contributions in mathematics:

◦ Ramanujan’s master theorem – widely used by

Ramanujan to calculate definite integrals and infinite series

◦ Described the first examples of mock theta functions in his last 1920 letter to G. H. Hardy and in his lost notebook.

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Godfrey Harold Hardy (1877 – 1947) and John Edensor Littlewood (1885 – 1977)

◦ Hardy was Ramanujan’s mentor and along with Littlewood, among the first people to discover Ramanujan’s genius

◦ Hardy and Littlewood collaborated extensively in works on mathematical analysis and analytic number theory Significant contributions in mathematics:

◦ Hardy-Littlewood circle method – developed to solve Waring’s problem

◦ Hardy-Littlewood maximal function – used to prove Lebesgue differentiation theorem, Rademacher

differentiation theorem, Fatou’s theorem on

nontangential convergence, and fraction integration theorem.

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Bertrand Russell (1872 – 1970)

◦ One of the founders of analytic philosophy along with Gottlob Frege, G. E. Moore, and Ludwig Wittgenstein.

◦ One of the 20^th century’s premier logicians

◦ Was awarded the Nobel Prize in Literature in 1950.

◦ Formed the Russell Tribunal in 1966 to investigate American military intervention in Vietnam

◦ Principia Mathematica, a three-volume work on the foundations of mathematics co-written with Alfred North Whitehead.

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Prasanta Chandra Mahalanobis (1893 – 1972)

◦ One of the members of the first Planning Commission of India

◦ The father of modern statistics in India.

◦ Founder of the Indian Statistical Institute.

◦ Mahalanobis distance – widely used in cluster analysis and classification techniques.

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Percy Alexander MacMahon (1854 – 1929)

◦ A former soldier turned mathematician, MacMahon was a pioneer in recreational mathematics.

◦ MacMahon Master theorem (MMT) – used to derive binomial identities.

◦ Combinatory Analysis, the first major book in enumerative combinatorics.

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Sir Isaac Newton (1642 – 1726)

◦ One of the most influential scientists of all time and a key figure in the scientific revolution.

◦ The best-known Master of the Mint (1700 – 1727)

◦ Was made President of the Royal Society in 1703.

◦ Knighted by Queen Anne in 1705.

◦ Generally credited along Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

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Leonhard Euler (1707 – 1783)

◦ A Swiss mathematician, widely considered as the most prolific as his collected works filled up 92 volumes.

◦ Introduced the concept of function, the letter Σ for summations, the letter i for imaginary unit, and

popularized the Greek letter π for the ratio of a circle's circumference to its diameter

◦ The only mathematician to have two numbers named after him: Euler’s number (e) and Euler-Mascheroni constant γ (gamma)

◦ Pioneered the use of analytic methods to solve number theory problems, thereby introduced a new field of study, analytic number theory

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Carl Gustav Jacob Jacobi (1804 – 1851)

◦ The first Jewish mathematician to be appointed professor at a German university.

◦ The younger brother of engineer and physicist, Moritz von Jacobi

◦ The first to apply elliptic functions to number theory

◦ One of the early founders of the theory of determinants.

◦ One of the first to introduce and study the Schur polynomials

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LESSONS THAT CAN LEARN FROM THIS STORY

1. Never stop dreaming, never give up, and never stop learning

Every day there are new opportunities to realize your dreams, so don’t waste it. The dream is to find yourself, find the goal and live a life that you do not regret. If you stop dreaming, you will not be able to truly live, and when you grow up, you will regret your unconvincing dreams.

In this film we see when self-taught mathematical genius Srinivasa Ramanujan fails out of college, he does not give up hope. Determined to pursue his passion, he contacts Professor G H Hardy and is invited to attend Trinity College. Although working together with Professor G H Hardy, Ramanujan get a lot of obstacles but he doesn’t give up, he will find a way to solve the obstacles.

The mathematical formula created by Ramanujan did not receive people’s attention at first, just because those people can’t understand the process of finding the answer. After that, Ramanujan discuss together with Professor G H Hardy. After a lot of hard work, Ramanujan finally created a simple and understand mathematical formula and last Ramanujan got everyone’s approval. Last but not least, geniuses already need to work so ward to realize their dreams, so we must need to work harder and don’t forget never stop dreaming, never give up and never stop learning.

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2. Love is enduring

 Ramanujan wife is one of his family that’s always support all of his work although the world is despise him. This show us how the world is working and who else that really sincere to be with us. His wife show that she is very love Ramanujan that she will never married again after Ramanujan is dead.

3. Appreciate relationship

 The professor who is Ramanujan best friend take care of Ramanujan while

he is coma. He also help him to become one of the fellowship although he

know that will make his loses his chance to get a high position.

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4. The need of being proactive in self-exploration

There is no horizon in the sea of learning, indeed applied to a young man who lived in poverty.

Ramanujan was born in an impoverished family, in that case he was not well educated. Even so, can’t deny that he was a self-made genius in mathematics. Throughout his persistent spirit, we can learn the importance of exploration in the progress of craving for new things. Cherish the perseverance and willpower, aiming for a fruitful pursuit in term of hard work and determination.

Knowing others is intelligence, but knowing yourself is true wisdom: By right act as a proof to Ramanujan himself. The process of getting to explore yourself isn’t an easy task. And yet, Ramanujan preferred to spend energy and time to yearn for his knowledge and potential mathematical concepts. From his experience, we can see without the significance of being diligent, it won’t contribute him to succeed. Thus, we should practice positive mindset to further develop our capability, so that we can always be prepared to adapt for any challenging tasks in the future.

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